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This idea comes from a functional pearl called "Power Series, Power Serious" [0], which is well worth reading.

I implemented the same thing myself in F#. [1]

[0]: https://citeseerx.ist.psu.edu/document?repid=rep1&type=pdf&d...

[1]: https://github.com/brianberns/PowerSeries

Huh, there must have been something in the water leading up to this. Also from 1998 is this paper, "Calculus in coinductive form" and neither of these cites the other. https://ieeexplore.ieee.org/document/705675

These are indeed very similar. Thanks for the link!

The math is a bit over my head, but this formulation seems more difficult than the one I'm familiar with. For example, x^2 is represented as 0::0::2 instead of 0::0::1 (because 2! = 2) and x^3 is represented as 0::0::0::6 instead of 0::0::0::1 (because 3! = 6). Is there a benefit to that?

I was introduced to the notion of power series two weeks ago, and now it's seemingly everywhere...

Power series have been everywhere for 200 years!

I am learning that indeed.

Power series are possibly one of the most powerful tools in analysis.

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